Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
338 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D8×Dic34 | C2 | semidirect |
| 2. #14531007 | C2 | semidirect |
| 3. #14528141 | C2 | semidirect |
| 4. #14526838 | C2 | semidirect |
| 5. #14526762 | C2 | semidirect |
| 6. #14526745 | C2 | semidirect |
| 68. D8×C17 | SD16 | semidirect |
| 110. Dic34 | D16 | semidirect |
| 189. C17 | #12352 | semidirect |
| 206. D8 | #63229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic34 | 2 |
| #14531007 | 2 |
| #14528141 | 2 |
| #14526838 | 2 |
| #14526762 | 2 |
| #14526745 | 2 |
| C17×#2206 | 2 |
| #12352 | 17 |